Why 27.306(x)^2 - 238.96(x) + 510.08?

To get ArcGIS to properly calculate the radius of the buffers for each earthquake I looked at Keefer, 1984 - Landslides caused by earthquakes. In his paper he noted that with an increase in earthquake magnitude landslides occurred in a larger area around the epicenter. I had to work backwards from one of his figures (Figure 2B) as he gave no formula for the curves in his figures. 

Keefer, 1984 Figure 2B

I snipped the figure out of the PDF and brought it into Illustrator. I could now find out what the distance from the epicenter each magnitude was plotted as. I made a grid and measured the distances, and with a little algebra could find out each one. I then plotted those into Excel and had it make me a curve. Finding that curve by hand would have been rather difficult. 

Keefer's curve as plotted in Excel. 

The curve was polynomial with the formula being y = 27.3606(x)^2 - 238.96(x) + 510.08. This is pretty close. It is actually gives a value a bit larger than what it should truly be. As you can see the trend line matches more closely beginning around a magnitude of 7 and above. I tested it using a magnitude of 7 which had an original value of 163. The formula gave 175. Close enough. A little large is probably better than smaller. One important thing to note is that earthquakes with a magnitude below 5.06 cannot be used. This is because the calculation gives a negative number below 5.06. 

These columns were added to ease computation of the radius.

To make this whole this work I had to make new fields in the attribute table. I found it worked best when I used one for 27.306(magnitude)^2, 238.96(magnitude), and 510.08 as its own column. For whatever reason ArcGIS didn't like to calculate correctly when I plugged in the formula straight forward. So I broke it into pieces and fed each one back in. It also calculated the radius of the buffer circle in meters, so I had to convert to km by multiplying by 1000. These buffers were way bigger than I would have expected. For a magnitude 7 it drew a circle 350 km in diameter!

Just about anywhere along the Alaskan coast would have been suitable, however a larger city seemed more suitable for this study.